An existence result for a model of complete damage in elastic materials with reversible evolution

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• 作者：Elena Bonetti ; Francesco Freddi ; Antonio Segatti
• 关键词：Complete damage ; Phase transition ; Non ; smooth PDE system ; Existence result for weak solutions
• 刊名：Continuum Mechanics and Thermodynamics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：29
• 期：1
• 页码：31-50
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Classical and Continuum Physics; Engineering Thermodynamics, Heat and Mass Transfer; Theoretical and Applied Mechanics; Structural Materials;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-0959
• 卷排序：29

文摘

In this paper, we consider a model describing evolution of damage in elastic materials, in which stiffness completely degenerates once the material is fully damaged. The model is written by using a phase transition approach, with respect to the damage parameter. In particular, a source of damage is represented by a quadratic form involving deformations, which vanishes in the case of complete damage. Hence, an internal constraint is ensured by a maximal monotone operator. The evolution of damage is considered “reversible”, in the sense that the material may repair itself. We can prove an existence result for a suitable weak formulation of the problem, rewritten in terms of a new variable (an internal stress). Some numerical simulations are presented in agreement with the mathematical analysis of the system.